@ Nollaig MacKenzie
Well I think I can answer your question: there is no need to submit the
sequence, since it already known.
First I had to fiddle out what a (non)degenerate truth table was and was
enlightened on this subject by Wittgenstein himself!
Then I found out what the formula was to generate the numbers of non-degenerate
truth tables, it appeared to be
(](4 : ('+/(_1^(x-y)) * (y!x) * 2^2^y')) i.@>:)"0 >:i.8x
2 10 218 64594 4294642034 18446744047940725978
340282366920938463334247399005993378250
which coincides with A000371, from which the second line reads " Number of
nondegenerate Boolean functions of n variables."
I still don't grasp what your concept of self-duality is.
R.E. Boss
> -----Oorspronkelijk bericht-----
> Van: Chat <[email protected]> Namens Nollaig
> MacKenzie
> Verzonden: dinsdag 20 augustus 2019 06:17
> Aan: [email protected]
> Onderwerp: Re: [Jchat] Number of self-dual arrays of rank N; OEIS
>
> It is a simple slip. T is, in the NOTE:
>
> 0 0
> 0 1
>
> 0 1
> 1 1
>
> And (let us call it Tlocs):
>
> ]Tlocs=:Gloc L:0 (0;1)=L:0 T
> ┌─────┬─────┐
> │0 0 0│0 1 1│
> │0 0 1│1 0 1│
> │0 1 0│1 1 0│
> │1 0 0│1 1 1│
> └─────┴─────┘
>
> If you then do the |. on the second item of Tlocs:
>
> (0{Tlocs),|.L:0 (1{Tlocs)
> ┌─────┬─────┐
> │0 0 0│1 1 1│
> │0 0 1│1 1 0│
> │0 1 0│1 0 1│
> │1 0 0│0 1 1│
> └─────┴─────┘
>
> You have the result you want.
>
> (I should mention that Gloc is meant to apply to arrays of 0 and 1. I should
> really have defined it as, perhaps, ($ #: I.@,)@:*
>
> Best wishes, N.
>
> On 2019.08.19 09:52:02, you,
> the extraordinary R.E. Boss, spake thus:
>
> > I tried to understand what you wrote and am left with questions.
> >
> > Take
> > [T=:(0 1 1, 1 0 1, 1 1 0,:1 1 1);0 0 0,0 0 1,0 1 0,:1 0 0
> > +-----+-----+
> > |0 1 1|0 0 0|
> > |1 0 1|0 0 1|
> > |1 1 0|0 1 0|
> > |1 1 1|1 0 0|
> > +-----+-----+
> >
> > With Gloc=: $ #: I.@, from the Journal of J, I get
> > Gloc L:0 (0;1)=L:0 T
> > +---+---+
> > |0 0|1 2|
> > |1 1|2 1|
> > |2 2|3 0|
> > +---+---+
> > From this I get
> > (, (>:@$|"1 -.)L:0,:~-.L:0)Gloc L:0 (0;1)=L:0 T
> > +-----+-----+
> > |0 0 |1 2 |
> > |1 1 |2 1 |
> > |2 2 |3 0 |
> > +-----+-----+
> > | 1 1| 0 _1|
> > | 0 0|_1 0|
> > |_1 _1|_2 1|
> > +-----+-----+
> > |1 1 |0 2 |
> > |0 0 |3 0 |
> > |3 2 |2 1 |
> > +-----+-----+
> > Which are the original locations of 0 and 1 respectively, there negations
> > (-.),
> and these converted to locations.
> > Being selfdual we should have the first and the reversed latest row to be
> equal, however
> > (-: [:|. (>:@$|"1 -.)L:0)Gloc L:0 (0;1)=L:0 T
> > 0
> >
> > What do I do wrong?
> >
> >
> > R.E. Boss
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